Success of SE simulations

I've heard stories about how computer simulations can be used to deal with some quantum mechanical systems, that cannot be solved exactly (for example systems with 10, 20, or 100 interacting particles) even though the number of particles is small enough that some explicit solutions do exist in principle. However, it has not become clear to me how successful these techniques have been. For example, have the spectrum of some heavier atoms, or some molecules, been solved correctly purely from the theory?